Question

The sum of the three terms of an Ap is 24 and the sum their cubes is 288. find those three terms of an Ap

Answer 1

Answer:

the given qn is wrong .the sum of three term should be 12

Step-by-step explanation:

please check the image for solution

Answer 2

AP is 2, 4, 6.

Step-by-step explanation:

Let the three terms be a-d, a, and a+d.

Given Sum of AP = 24

a-d + a + a+d = 24/2

3a = 12

Therefore a = 4 ---------------------(1)

Sum of cubes = 288

(a-d)³ + a³ + (a+d)³ = 288

[a³ -d³ -3ad (a+d)] + a³ + [a³ + d³ + 3ad (a- d)] = 288

3a³ + 6ad² = 288

Substituting a = 4, we get:

3 * 64 + 24d² = 288

24d² = 288 - 192

d² = 96/ 24

d = root of 4

d = 2

So the terms are 4-2, 4 and 4 + 2.

AP is 2, 4, 6.